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Consider four steel wires of dimensions given below $(d = d i a m e t e r a n d l = l e n g t h) :$
1) $l = 1 m, d = 1 m m$ 2) $l = 2 m, d = 2 m m$ 3) $l = 2 m, d = 1 m m$ 4) $l = 1 m, d = 2 m m$
If same force is applied to all the wires then the elastic potential energy per unit volume stored will be maximum in wire:

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answer is C.

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Detailed Solution

We have, $U = \frac{F^{2}}{2 k}$
Where $k = \frac{Y l}{A} = \frac{Y l}{\frac{1}{4} π d^{2}} ∴ U \propto \frac{d^{2}}{l}$

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